Adding Bend Modifier for a parent object and treating as if it's a single object
As explained in the comment, you can use a lattice to do that.

The idea is the following:


Create a lattice and scale it appropriately (1x2, as for the plane mentioned in this answer). Scale it in object mode (edit mode will give a bad result deforming the curves later).
Give it the resolution you want, ie 20x40x1





Bend it using 2 empties





Now add your curves, rotate and scale them to fit the same size as the lattice
Add a lattice modifier to one of the curves
Then link the modifier to the others CtrlL then 'modifiers'




edit the blend file:


Concerning Russia, I think this is due to that:

If you convert it to mesh, lines are going east/west for a long distance, so when bent, that does not work: "these lines are like the string of a bent bow"